Known lubricating systems for spindle bearing assemblies include one which is called oil-mist lubrication wherein lubricating oil is atomized and delivered to the spindle bearing with compressed air and one which is called oil-jet lubrication wherein pressurized lubricating oil is directed onto the spindle bearing at high speed. In these lubricating methods the lubricating and cooling of the spindle bearing is generally carried out at the same time through the flow of the lubricating oil. However, in the oil-jet lubrication, the lubricating oil is directed onto the spindle bearing at such high speed that mechanical losses such as friction resistance in the sliding portion of the spindle bearing or viscous resistance of the lubricating oil are developed. This mechanical loss is especially developed by the high speed of the grinding wheel spindle of a cylinder grinding machine. Therefore, the less volume of lubricating oil supplied in order to reduce the mechanical losses, the worst the heat absorption becomes. Accordingly the spindle bearing is apt to be subjected to the danger of heating up. On the other hand, the greater the volume of the jetted lubricating oil in order to improve the cooling effect the greater such mechanical loss becomes. There is thus a mutually inconsistant drawback between the cooling and the lubricating through the volume of the jetted lubricating oil so that it is difficult to control both the cooling and lubricating at satisfactory levels.